

A081611


Number of numbers <= n having no 2 in their ternary representation.


6



1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16
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OFFSET

0,2


COMMENTS

a(n) + A081610(n) = n+1.
a(n) is also the size of the subset of [1...n] when numbers are added greedily so as to not contain a 3term arithmetic progression, i.e., according to A003278: a(n) = the largest k such that A003278(k) <= n. (Cf. A003002, the size of the optimal (largest) 3free subset of [1...n]).  R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 19 2009


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000


FORMULA

G.f. A(x) satisfies A(x)=(1+x)(1+x+x^2)A(x^3).  Michael Somos, Aug 31 2006
G.f.: (1/(1x))Product{k>=0} 1+x^(3^k).  Michael Somos, Aug 31 2006
a(n)=a(n1)+A039966(n).  Michael Somos, Aug 31 2006


PROG

(PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=3; A=(1+x)*(1+x+x^2)*subst(A, x, x^3)); polcoeff(A, n))} /* Michael Somos, Aug 31 2006 */
(PARI) first(n)=my(s, t); vector(n, k, t=Set(digits(k, 3)); s+=t[#t]<2) \\ Charles R Greathouse IV, Sep 02 2015
(Haskell)
a081611 n = a081611_list !! n
a081611_list = scanl1 (+) a039966_list
 Reinhard Zumkeller, Jan 28 2012


CROSSREFS

Cf. A007089, A081603, A081608, A061392.
Number of terms in A003278 that are <=n.  R. Shreevatsa (shreevatsa.public(AT)gmail.com), Oct 19 2009
Sequence in context: A303997 A276646 A029130 * A297995 A081228 A270826
Adjacent sequences: A081608 A081609 A081610 * A081612 A081613 A081614


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Mar 23 2003


STATUS

approved



